Translation of abstract (English)

We present a series of evolutionary calculations for stars of population III with 2 to 10 solar masses from the main sequence to helium shell burning. Two of these models are continued onto the thermally pulsing asymptotic giant branch (TPAGB). We observe thermal pulses, third dredge-up and hot bottom burning as well as the »carbon ingestion flash«; the latter is exclusive to extremely metall poor stellar models: During a thermal pulse, an additional convection zone above the hydrogen shell source develops. This convection zone touches carbon rich layers and thus induces the influx of carbon into the extremely carbon poor hydrogen shell source. Hence, hydrogen burning via the CNO-cycle is strongly enhanced, and both shell sources reach an activity maximum at the same time. This phenomenon only occurs during the very first thermal pulses; the stellar envelope is soon enriched due to the third dredge-up, such that the further evolution is normal. The relations between core mass and luminosity as well as interpulse period in our extremely metall poor models deviate from the solar case: The luminosity is lower by 10 to 30%, the interpulse period longer by a factor 6 to 10. The presented code takes the time dependence of convective mixing into account and solves all equations of stellar structure and evolution implicitly and simultaneously.